14949 + Interview Questions in Maths in Class 11 Page 95 InterviewSolution

4701.	Find (dy)/(dx)if x =a ( theta - sin theta ), y = a ( 1 - cos theta ).
Answer» ANSWER :`COT ((THETA)/(2))`

Discussion

4702.	-3 le (4 - (3x))/(-5) le 2
Answer» ANSWER :`[-4,2]`

Discussion

4703.	Which of the following are meaningful ?
Answer» `barmu.(barvxxbaromega)` `(barmu.barv).baromega` `barmu.(barv.baromega)` 1 or 3 Answer :A

Discussion

4704.	If f (x) = (x ^(2 ) -10/( x ^(2) +1))), for every real numbers. Then the minimum vlaue of f
Answer» Does not exist because f is BOUNDED Is not ATTAINED even through f is bounded Is EQUAL to `+1` Is equal to `-1` ANSWER :D

Discussion

4705.	If ABCD is a quadrillateral such that vec(AB) = vec(i) + 2vec(j), vec(AD)= vec(j) + 2vec(k) and vec(AC)= 2 (vec(i) + 2vec(j)) + 3(vec(j) + 2vec(k)), then area of the quadrilateral ABCD is
Answer» `(5 sqrt21)/(2)` `(3 sqrt21)/(2)` `(sqrt21)/(2)` `(7)/(2)` ANSWER :C

Discussion

4706.	Differentiate the following w.r.t. x or t or u as the case may be: y = (x^5 - x +2)/( x^3 + 7)
Answer» ANSWER :`(DY)/( DX) = (2x^7 + 35x^4 + 2x^3 - 6x^23 - 7)/( (x^3 + 7)^2)`

Discussion

4707.	If (3x, x + y) =( 6,3), find x and y
Answer» SOLUTION :X = 2,y = 1

Discussion

4708.	If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2)then k=
Answer» `1//2` `1` `3//2` `2` ANSWER :C

Discussion

4709.	If A + B = 135^(@) then (TanA.TanB)/((1+TanA)(1+TanB)) =
Answer» 0 1 2 `1//2` ANSWER :D

Discussion

4710.	Line y = 2x I chord of the circle x^(2) + y^(2) - 10x = 0. Derive equaiton of the circle whose diameter is chord.
Answer» ANSWER :`x^(2) + y^(2) - 2x - 4Y = 0`

Discussion

4711.	The slant height of a cone is fixed at 7cm. The rate of increase in the volume of the cone corresponding to the rate of increases of 0.3 cm/s in the hieght when h = 4cm is
Answer» `(PI)/(10)` C c/s `(3PI)/(10)` c c/s `(pi)/(5)` c c/s `(7pi)/(10)` c c/s Answer :A

Discussion

4712.	Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means.
Answer» ANSWER :22.85

Discussion

4713.	Foot of the perpendicular draw from (7,6) on y-axis is
Answer» (0,6) (7,0) (-7,-6) (6,7) ANSWER :A

Discussion

4714.	Evaluate the following limits : Lim_(h to 0 ) ([sqrt(x+h)-sqrt(x)])/h
Answer» ANSWER :`1/(2sqrt(X))`

Discussion

4715.	Find the general solution of the following equations : sec^(2)2x=1-tan2x
Answer» Answer :`X = (NPI)/( 2), or (npi)/(2) + ( npi)/(2) + (3PI)/(8), n in Z`

Discussion

4716.	Three coins are tossed once. Let A denote the event three heads show'', B denote the event ''two heads and one tail show'', C denote the event'' three tails show and D denote the event 'a head shows on the first coin''. Which events are: (i) mutually exclusive ? (ii) simple ? (iii) Compound ?
Answer» ANSWER :`:. ` B and D are COMPOUND EVENTS.

Discussion

4717.	(1+i)^(4)+(1-i)^(4) = ........ .
Answer» ANSWER :`-8`

Discussion

4718.	f(x) = (3 sin x - sin (3x))/(x^(3)) , x ne 0 , f(0) = 4at x = 0 , f is
Answer» discontinuous not DETERMINED CONTINUOUS NONE ANSWER :C

Discussion

4719.	If {:((n),(r)):}=(n!)/(k), then K =.......
Answer» `R !` `(n-n) !` `(n-n) ! R!` `(r(n-1))!` ANSWER :C

Discussion

4720.	If the equation 2xy + gx + fy + 5 = 0 repre sents a pair of lines, then fg=
Answer» 1 10 5 0 Answer :B

Discussion

4721.	cos^(2)(7(1^@)/(2))-cos^(2)(37(1^(@))/(2))= …………
Answer» `(3)/(4)` `(2)/(SQRT(2))` `(1)/(2)` `(1)/(2sqrt(2))` ANSWER :D

Discussion

4722.	Given that z=1-i
Answer» ANSWER :`((1)/(2),(1)/(2))`

Discussion

4723.	The ratio in which the plane vecr ( veci -2 hatj + 3 hatk) = 17 divides the line joining the points - 2vec i + 4 vecj + 7 veckand 3 veci - 5 vecj + 8 veck is
Answer» `1:5` `1:10` `3:5` `3:10` ANSWER :D

Discussion

4724.	Write the following sets in the roaster form. A= {x : x in R, 2x+11 = 15}
Answer» ANSWER :`X= 2`

Discussion

4725.	At .........height one can reach by walking x mets with slope 30^@ and with height y met.
Answer» ANSWER :`2Y`

Discussion

4726.	Find the coefficient of : x^(4) " in " (2x+5)^(8)
Answer» ANSWER :700000

Discussion

4727.	lim_(xto1)(1-x)tan (xpi/(2))=………
Answer» `(PI)/(4)` `(pi)/(2)` `(2)/(pi)` `(4)/(pi)` ANSWER :C

Discussion

4728.	IfP=(1/(X_p),p),Q=P=(1/(X_q),q),R=(1/(x^r),r) " where " x_k ne 0, " dentoes the " k^th term of H.p. for k in N, then
Answer» AREA of `DeltaPQR=((p^2q^2r^2)/2)SQRT((p-q)^2+(q-R)^2+(r-p)^2))` `DeltaPQR` is a right angled triangle. The points P,Q,R are collinear `DeltaPQR` is EQUILATERAL triangle Answer :C

Discussion

4729.	A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?
Answer» ANSWER :1632

Discussion

4730.	x = log (1/y + sqrt(1+1/y^2)) rArr y =
Answer» TAN hx COT hx SEC hx cosec hx Answer :D

Discussion

4731.	If (sqrt(2)x+sqrt(3)y)^(2)-36(sqrt(3)x-sqrt(2)y)^(2)=0 and sqrt(2)x+sqrt(3)y+4sqrt(5)=0represents an Isosceles triangle with base angle tan^(-1)6 then its area is
Answer» 4 `8//3` `8sqrt(6)` 9 Answer :B

Discussion

4732.	The radius and height of a cone are measured as 6cms each by scale in which there is an error of 0.01 cm in each cm. Then the approximate error in its volume is
Answer»

Discussion

4733.	Calculate the standard deviation of the following given in the following table.
Answer» ANSWER :3.68

Discussion

4734.	Sketchthe regionenclosed by y= sin x y =cos x=axisin [0,pi]
Answer» ANSWER :`(##AKS_NEO_CAO_MAT_XI_VIA_P02_C05_E03_007_A01##)`

Discussion

4735.	How many 5-digits telephone numbers can be formed with the digits 0,1,2,….,8,9 if each numbers starts with 35 and no digit appears more than once?
Answer» Answer :` ""^(8)P_3 = 336` FIRST 2 places are fixed and remaining =3 places can befilled in ` ""^(8)P_3 ` ways

Discussion

4736.	Differentiate the following w.r.t. x or t or u as the case may be: s= t^(2) ( t+1)^(-1)
Answer» ANSWER :`(DS)/( DT ) = (t^2 + 2T )/( (t+1)^2)`

Discussion

4737.	Three dice are thrown simultaneously. Find the sample space
Answer» SOLUTION :{(1,1,1),(1,1,2),.......,(6,6,6)}

Discussion

4738.	Evaluate the following limits : Lim_(x to 1) (x^(4) - 3x^(3) +2)/(x^(3)-5x^(2)+3x+1)
Answer» ANSWER :`5/4`

Discussion

4739.	Assertion (A) , The lines representant by 3x^(2)+10xy+3y^(2)-16x-16y+16=0 and x+y=2 do not form a triangle Reason (R) : the above the three lines concurrent at (1,1)
Answer» Both A and R are true and R is the CORRECT explanation A Both A and R are true but R is not the correct explanation of A A is true but R is false A is false but R is true Answer :A

Discussion

4740.	A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month
Answer» ANSWER :8080

Discussion

4741.	A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earning during the first year?
Answer» ANSWER :RS 83,520

Discussion

4742.	If k is the diameter of a circle and A is the area of a sector of the circle whose vertical angle is theta then (dA)/(dt) =
Answer» `(k^(2))/(8)((d theta)/(dt))` `((k^(2))/(4))((d theta)/(dt))` `(d theta)/(dt)` `k((d theta)/(dt))` Answer :A

Discussion

4743.	If cos alpha = (-3)/5 and sin beta = 7/25 where (pi)/2 lt alpha lt pi and 0 lt beta lt (pi)/2 then find the values of tan (alpha + beta) and sin (alpha + beta).
Answer» ANSWER :`(-3)/(4),(3)/(5)`

Discussion

4744.	From the curve y= sinx, graph the function (i) y=sin(-x) (ii)y=-sin(-x) (iii) y=sin(pi/2+x) which is cos x (iv) y=sin(pi/2-x) which is also cos x (refer trigonometry)
Answer» ANSWER :`-SIN X=f(x)`

Discussion

4745.	Evaluate the following limits : Lim_(x to oo) ((x-1)/(x+1))^(2)
Answer» ANSWER :`E^(-2)`

Discussion

4746.	Find the domain and range of the function f(x)=[sinx]
Answer» ANSWER :`D_(F)=R`, `R_(f)={-1,0,1}`

Discussion

4747.	If x,y are strictly positive such that x+y=1 then the minimum value of xlogx+ylogy is
Answer» LOG2 `-log2` 2log2 0 Answer :B

Discussion

4748.	Find (dy)/(dx)if x = log t + sin t, y= e ^(r ) + cos t.
Answer» ANSWER :`( t (E ^(t) -SIN t ))/( 1 + t COS t)`

Discussion

4749.	Find the approximations of the following root(3)(65)
Answer» ANSWER :4.02208

Discussion

4750.	Find the sum: 1 + (1)/(2) (1 + 2) + (1)/(3) (1 + 2 + 3) +……up to 16 terms.
Answer» ANSWER :76

Discussion

Explore topic-wise InterviewSolutions in .

Find (dy)/(dx)if x =a ( theta - sin theta ), y = a ( 1 - cos theta ).

-3 le (4 - (3x))/(-5) le 2

Which of the following are meaningful ?

If f (x) = (x ^(2 ) -10/( x ^(2) +1))), for every real numbers. Then the minimum vlaue of f

If ABCD is a quadrillateral such that vec(AB) = vec(i) + 2vec(j), vec(AD)= vec(j) + 2vec(k) and vec(AC)= 2 (vec(i) + 2vec(j)) + 3(vec(j) + 2vec(k)), then area of the quadrilateral ABCD is

Differentiate the following w.r.t. x or t or u as the case may be: y = (x^5 - x +2)/( x^3 + 7)

If (3x, x + y) =( 6,3), find x and y

If 2^(3) + 4^(3) + 6^(3) + … + (2n)^(3) = kn^(2) ( n+1)^(2)then k=

If A + B = 135^(@) then (TanA.TanB)/((1+TanA)(1+TanB)) =

Line y = 2x I chord of the circle x^(2) + y^(2) - 10x = 0. Derive equaiton of the circle whose diameter is chord.

The slant height of a cone is fixed at 7cm. The rate of increase in the volume of the cone corresponding to the rate of increases of 0.3 cm/s in the hieght when h = 4cm is

Coefficient of variation of two distributions are 60 and 70, and their standard deviations are 21 and 16, respectively. What are their arithmetic means.

Foot of the perpendicular draw from (7,6) on y-axis is

Evaluate the following limits : Lim_(h to 0 ) ([sqrt(x+h)-sqrt(x)])/h

Find the general solution of the following equations : sec^(2)2x=1-tan2x

Three coins are tossed once. Let A denote the event three heads show'', B denote the event ''two heads and one tail show'', C denote the event'' three tails show and D denote the event 'a head shows on the first coin''. Which events are: (i) mutually exclusive ? (ii) simple ? (iii) Compound ?

(1+i)^(4)+(1-i)^(4) = ........ .

f(x) = (3 sin x - sin (3x))/(x^(3)) , x ne 0 , f(0) = 4at x = 0 , f is

If {:((n),(r)):}=(n!)/(k), then K =.......

If the equation 2xy + gx + fy + 5 = 0 repre sents a pair of lines, then fg=

cos^(2)(7(1^@)/(2))-cos^(2)(37(1^(@))/(2))= …………

Given that z=1-i

The ratio in which the plane vecr ( veci -2 hatj + 3 hatk) = 17 divides the line joining the points - 2vec i + 4 vecj + 7 veckand 3 veci - 5 vecj + 8 veck is

Write the following sets in the roaster form. A= {x : x in R, 2x+11 = 15}

At .........height one can reach by walking x mets with slope 30^@ and with height y met.

Find the coefficient of : x^(4) " in " (2x+5)^(8)

lim_(xto1)(1-x)tan (xpi/(2))=………

IfP=(1/(X_p),p),Q=P=(1/(X_q),q),R=(1/(x^r),r) " where " x_k ne 0, " dentoes the " k^th term of H.p. for k in N, then

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways﻿ can this be done when the committee consists of:﻿ (i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?﻿

x = log (1/y + sqrt(1+1/y^2)) rArr y =

If (sqrt(2)x+sqrt(3)y)^(2)-36(sqrt(3)x-sqrt(2)y)^(2)=0 and sqrt(2)x+sqrt(3)y+4sqrt(5)=0represents an Isosceles triangle with base angle tan^(-1)6 then its area is

The radius and height of a cone are measured as 6cms each by scale in which there is an error of 0.01 cm in each cm. Then the approximate error in its volume is

Calculate the standard deviation of the following given in the following table.

Sketchthe regionenclosed by y= sin x y =cos x=axisin [0,pi]

How many 5-digits telephone numbers can be formed with the digits 0,1,2,….,8,9 if each numbers starts with 35 and no digit appears more than once?

Differentiate the following w.r.t. x or t or u as the case may be: s= t^(2) ( t+1)^(-1)

Three dice are thrown simultaneously. Find the sample space

Evaluate the following limits : Lim_(x to 1) (x^(4) - 3x^(3) +2)/(x^(3)-5x^(2)+3x+1)

Assertion (A) , The lines representant by 3x^(2)+10xy+3y^(2)-16x-16y+16=0 and x+y=2 do not form a triangle Reason (R) : the above the three lines concurrent at (1,1)

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. Find his salary for the tenth month

A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earning during the first year?

If k is the diameter of a circle and A is the area of a sector of the circle whose vertical angle is theta then (dA)/(dt) =

If cos alpha = (-3)/5 and sin beta = 7/25 where (pi)/2 lt alpha lt pi and 0 lt beta lt (pi)/2 then find the values of tan (alpha + beta) and sin (alpha + beta).

From the curve y= sinx, graph the function (i) y=sin(-x) (ii)y=-sin(-x) (iii) y=sin(pi/2+x) which is cos x (iv) y=sin(pi/2-x) which is also cos x (refer trigonometry)

Evaluate the following limits : Lim_(x to oo) ((x-1)/(x+1))^(2)

Find the domain and range of the function f(x)=[sinx]

If x,y are strictly positive such that x+y=1 then the minimum value of xlogx+ylogy is

Find (dy)/(dx)if x = log t + sin t, y= e ^(r ) + cos t.

Find the approximations of the following root(3)(65)

Find the sum: 1 + (1)/(2) (1 + 2) + (1)/(3) (1 + 2 + 3) +……up to 16 terms.

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: (i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?